Classiication of Nonrigid Motion in 3d Images Using Physics-based Vibration Analysis

We present a method for comparison and classii-cation of nonrigid motion using a deformable model and the associated modal dynamics. Using the solid state physics formulation, we develop the equations of motion and the analytical expressions of vibration modes of a multidimensional elastically-deformable model that we use for tracking of nonrigid features in dynamic images. Thus, nonrigid motion of a 3D deformable object can be recovered in closed-form in modal space, by superimposing a few low-frequency modes that can be computed in a straightforward manner. We show that the deformation spectrum is a compact description of the deformation information, and allows deformation comparison and classiication. Examples on 2D and 3D medical images are presented. The contribution of the paper is making modal analysis an eecient and easy-to-use tool for nonrigid motion classiication. 1 Background Recently, many computer vision researchers have shown interest in nonrigid motion analysis, rst proposing improvements to a rigid-body interpretation 26, 24]. Following the theory of deformable models 10], physically-based modelling for nonrigid motion analysis has become extremely popular. Terzopoulos et al. use a dynamic deformable model to infer the 3D structure of nonrigid objects 23, 11]. Duncan et. al use bending energy and surface curvature to analyze nonrigid motion 1] (an alternative formulation can be found in 3]). In 13], nonrigid motion is assumed to be locally conformal, while Chen and Huang use a tensor based analysis to estimate global motion parameters and local deformation 6]. Superquadrics 20] have shown to be useful predeened shapes globally and locally deformable by using the equations of dynamics 12]. As to nonrigid motion analysis, our work is mainly related to the one of Pentland et al. 17, 16]. We make use of modal analysis, a well-known mechanical engineering technique, which consists in decomposing and approximating the motion in the free vibrations basis (modes) of the object. We introduce the deformation spectrum and show its use for comparing and classifying diierent deformations. The principal warps analysis of 5], the Fourier decomposition of 19, 21, 22], and the principal components analysis of 7] all show a similar spirit as our method. Finally, there is an analogy between our dynamic method of deformation comparison and the static method of shape comparison using Fourier shape de-scriptors (see 18] for a review). However, the 3D case developed by our model cannot be easily described by those considerations. 2 An elastically deformable model Let us …